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Flatten the Curve (SIR Model & Social Distancing)

Flatten the Curve (SIR Model & Social Distancing)
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2020-03-27 08:23
FunctionCalculusProbability & Statistics
This app simulates pandemics and social distancing based on the SIR model. It uses concepts from calculus and coordinate geometry to demonstrate how parameters can control the spread of an epidemic. It employs GeoGebra commands such as polynomial fitting and differential equation solving, suitable for high school and above students or educators.

GeoGebra Commands & Parameters

  1. OrthogonalLine((90, 0), xAxis) → t3
  2. Point(t3) → SD_{3}
  3. OrthogonalLine((60, 0), xAxis) → t2
  4. Point(t2) → SD_{2}
  5. OrthogonalLine((30, 0), xAxis) → t1
  6. Point(t1) → SD_{1}
  7. OrthogonalLine((0, 0), xAxis) → t0
  8. Point(t0) → SD_{0}
  9. Polynomial({SD_{0}, SD_{1}, SD_{2}, SD_{3}}) → SD
  10. NSolveODE({S', I', R'}, 0, {S_{0}, I_{0}, R_{0}}, TimeSpan) → SIRt, SIRt_{2}, SIRt_{3}
  11. Length(SIRt_{2}) → Ilen
  12. OrthogonalLine((120, 0), xAxis) → t4
  13. Point(t4) → SD_{4}
  14. OrthogonalLine((150, 0), xAxis) → t5
  15. Point(t5) → SD_{5}
  16. OrthogonalLine((180, 0), xAxis) → t6
  17. Point(t6) → SD_{6}
  18. OrthogonalLine((0, ICUbeds), yAxis) → ICU
  19. Textfield(Population) → PopulationInput
  20. Textfield(I_{0}) → I_0Input
  21. Textfield(R_{0}) → R_0Input
  22. First(SIRt_{2}, Ilen) → It
  23. FitPoly(It, 56) → Ipoly
  24. Textfield(CriticalRate) → CriticalRateInput
  25. Textfield(ICUbeds) → ICUbedsInput
  26. SelectedIndex(CountryList) → SelectedCountry
  27. Max(Ipoly, 0, TimeSpan) → ImaxP

AI Drawing Prompt Reference

Draw a graph simulating pandemic spread, including the x-axis and four points representing social distancing at 0, 30, 60, and 90 units from left to right. Fit a polynomial curve through these points, and simulate the epidemic spread with a differential equation showing the number of infected individuals over time. Add a vertical line above the x-axis for ICU beds and label the peak of the infected curve. Include input fields for population, initial infected, initial recovered, ICU beds, and critical rate, along with a dropdown menu to select countries.
The prompt above was compiled from the original drawing commands and is for reference only.